ICHITECTURA.L  PROPORTION 


ILLUSTRATED 


,  J.BRYAN 


ARCHITECTURAL 
PROPORTION. 


ILLUSTRATED. 


NEW   SYSTEM   OF   PROPORTION   SHOWING  THE  RELA- 
TION BETWEEN  AN  ORDER  OF  ARCHITECTURE 
AND  A  BUILDING  OF  ANY  KIND. 


RULES  FOR  FINDING  THE  HEIGHT  OF  FOUNDATIONS,  BASES,  WATER-TABLES,  WINDOW 
SILLS,  DOORS,  WINDOWS,  BALUSTRADES,  AND  SUPERIMPOSED  STORIES;  WIDTH 
OF  DOORS,  WINDOWS,  ARCHITRAVES,  PILASTERS  AND  POSTS;  HEIGHT  AND 
PROJECTION  OF  ENTABLATURES,  CORNICES,  AND  ALL  EXTERIOR 
FINISH;    ALSO   HEIGHT   OF   BASES,  WINDOW-STOOLS, 
HEIGHT  AND  PROJECTION  OF  STUCCO  CORNICES, 
AND   INTERIOR   FINISH,   WITH  MANY 
VALUABLE  TABLES. 


By  A.  J.  BRYAN,  Architect. 


SAN  FRANCISCO: 
A.  L.  BANCROFT  &  CO.,  PRINTERS  AND  LITHOGRAPHERS, 
721  Market  Street, 
1880. 


Copyright,  1880, 
Y  A.    J.  BRYAN. 


PREFACE. 


Very  few  general  rules  in  architectural  proportion  can  be  applied  to  every  style  of 
architecture.  Special  cases  can  only  be  provided  for  by  the  ingenuity  of  the  Architect. 
Our  aim  has  been  to  avoid  extremes,  and  furnish  only  such  practical  rules  as,  in  our  judg- 
ment, seem  best  adapted  to  the  requirements  of  all  classes  of  buildings  in  this  country. 
While  the  rules  and  plates  are  our  own,  it  is  but  just  to  say  that  we  have  freely  consulted 
the  works  of  many  authors  on  the  subject,  and  have  carefully  compared  the  practical 
results  from  other  and  more  complicated  rules  with  the  results  obtained  by  the  application 
of  the  simple  and  comprehensive  ones  contained  herein,  which,  added  to  our  own  experience, 
enables  us  to  offer  this  volume  to  the  Building  Fraternity  with  the  assurance  that  the 
measures  given  are  in  accord  with  the  works  of  the  best  masters.  The  tables  are  introduced 
in  the  belief  that  they  will  obviate  the  necessity  of  many  calculations,  acquaint  the  novice 
with  the  relative  proportions  of  the  members  of  a  column,  and  serve  as  a  ready  reference 
for  all  persons  who  are  interested  in  building. 

A.  J.  BRYAN. 

Chico,  California,  1880. 


Digitized  by  the  Internet  Archive 

in  2013 


http://archive.org/details/architecturalproOObrya 


CONTENTS. 


PLATE. 

Standard  of  Proportion   I 

The  Necessity  for  a  Proportional  Order  Illustrated   I 

Application  of  the  Proportions  of  the  Standard  to  a  Cottage   I 

Justification  of  the  Rules   I 

Detail  of  Side  Architrave  and  Window-stool       II 

Detail  of  Room  Skirting  or  Base   Ill 

Detail  of  Shaft-base   IV 

Detail  of  Pedestal  Cornice   V 

Detail  of  Capital   VI 

Detail  of  Entablature  Cornice   VII 

Detail  of  Cornice  without  Frieze  or  Architrave   VIII 

Detail  of  Architrave.   IX 

Superimposed  Stories   X 


PAGE. 

Architectural  Proportion,  where  it  can  exist  .'   6 

Origin  of  the  Five  Orders  of  Architecture   7 

Gradual  Development  of  the  Orders  of  Architecture     7 

Description  of  the  Standard  of  Proportion   10 

Equality  of  Ratios  between  Interior  and  Exterior  Finish   12 

Foundations,  Architects  should  Visit  the  Building  Site   12 

Appearance  of  a  Building  Dependent  on  Height  of  Foundation   13 

How  to  Find  the  Relative  Sizes  for  the  Interior  Finish  of  a  Story     15 

How  to  Find  the  Relative  Sizes  for  the  Verandah  Finish   15-17 

When  Minor  Members  should  be  Excluded  from  Entablatures   17 

Where  Entablatures  may  be  Properly  Used   19 

Reducing  the  Height  of  Superimposed  Stories  19-21 

Comparative  Table   23 

Height  of  Entablatures  Elevated  Above  Standard  Example  23-25 

Table  showing  Height  of  Entablatures   27 

Rules  28-29 

Tables  Giving  the  Height  of  Members  of  the  Interior  Finish,  for  Stories  of  One  Hundred  Different 

Heights   30-33 


ARCHITECTURAL  PRORORTION. 


That  the  ancient  Orders  of  Architecture  have  received  their  full  share  of  attention  from 
writers  in  all  ages  no  one  can  doubt.  Many  excellent  works  contain  elaborate  descriptions 
of  the  beautiful  proportions  of  the  Five  Orders,  and  merited  criticisms  on  the  present  styles, 
while  very  few  contain  any  practical  system  which  can  be  used  for  the  improvement  of 
the  interior  and  exterior  appearance  of  the  thousands  of  buildings  which  are  being  erected 
each  year  in  this  country. 

Architecture,  like  any  other  invention  of  man,  is  susceptible  of  improvement.  The 
finished  building  is  only  the  reflex  of  the  designer's  knowledge  of  the  fitness  of  things.  A 
justly  proportioned  building  is  pleasing  to  the  eye,  while  it  has  no  part  that  will  attract 
particular  attention — a  finely  formed  body,  with  ornaments  of  natural  form  and  members  of 
just  magnitude. 

Architectural  proportion  is  the  relation  one  part  or  member  of  a  building  bears  to 
others,  and  can  exist  only  in  the  combination  of  a  number  of  things  of  unequal  size.  A 
square  building  has  no  proportion  between  length,  width  and  height,  and  at  best  is  a  poor 
example  of  architecture. 

The  student  cannot  devote  too  much  time  to  the  study  of  the  best  examples  of  classical 
architecture,  yet,  after  all  his  study  and  research,  when  he  is  called  upon  to  design  dwellings 
and  other  buildings  which  are  suited  to  the  requirements  of  modern  civilization,  he  may  be 
able  to  talk  learnedly  about  architecture  as  an  art,  and  still  have  no  idea  how  his  knowledge 
of  ancient  architecture  will  enable  him  to  give  just  proportions  to  the  members  of  an 
ordinary  building. 

High  art  is  a  popular  text  for  much  writing,  but  unfortunately  those  who  discourse 
most  upon  that  worthy  theme  seem  to  practice  it  with  the  least  degree  of  intelligence  in 
their  designs.  Unnatural  forms  in  ornamentation  and  uniform  widths  for  the  members  of 
stories  of  different  heights,  which  are  so  often  found  in  the  designs  of  impracticable  theorists, 
are,  of  themselves,  a  bar  to  pleasant  variety  in  a  design,  and  the  essence  of  bad  taste  in 
architecture. 


ARCHITECTURAL  PROPORTION. 


7 


As  the  proportions  of  classic  architecture  are  not  applicable  to  modern  buildings,  or  to 
cheap  buildings  of  any  style,  new  ratios  must  be  introduced,  so  as  to  modify  the  ancient 
Orders,  or  produce  new  ones.  The  Five  Orders  of  Architecture,  known  as  the  Doric,  Ionic, 
Corinthian,  Tuscan  and  Composite,  were  each  suited  to  a  particular  purpose  and  style  of 
building. 

After  the  return  of  the  Heracleida?,  the  Dorians,  who  afterwards  founded  Sparta,  Argos 
and  Messenia,  introduced  the  Doric  Order  into  the  Peloponesus,  about  1104  B.  C.  That  they 
were  the  first  inventors  of  that  Order  is  very  probable,  because  the  massive  proportions  -of 
the  earliest  examples  were  particularly  suited  to  the  purposes  of  architecture  in  the 
Peloponesus  during  the  reign  of  the  Hellenic  tribes. 

The  Ionic  colonies  of  Asia  Minor  gratified  their  taste  and  supplied  their  wants,  in  an 
architectural  sense,  by  introducing  the  Order  which  bears  their  name.  The  Greek  Archi- 
tects, Callicrates,  Ictinus,  Pericles  and  Phidias,  built  the  celebrated  Parthenon  at  Athens, 
in  the  Doric  Order,  about  440  B.  C,  and  Callicrates  is  credited  with  inventing  the  Corinthian 
Order,  which  was  not  in  general  use  in  Greece  before  the  time  of  Alexander  the  Great;  the 
oldest  example  in  Greece  being  the  Choragic  Monument  of  I^ysicrates,  built  335  B.  C. 

The  l\iscan  Order  is  of  doubtful  origin,  and  was  probably  never  extensivelv  used,  while 
the  Triumphal  Arches  erected  by  the"  Romans  to  commemorate  great  victories,  brought  into 
use  the  excessively  ornamented  column  known  as  the  Composite  Order. 

If  we  go  further  back  into  the  history  of  architecture  and  take  account  of  Assyrian 
Architecture  on  the  plains  of  Mesopotamia;  Egyptian  Architecture  as  applied  to  the  temples  of 
the  Theban  kings,  of  whom,  Osirtesen  reigned  1640  B.  C,  we  are  led  to  believe  that  archi- 
tecture was  reduced  to  something  like  a  science  long  before  even  the  Doric  Order  was  invented. 

In  ancient  architecture,  the  column  was  the  prominent  feature,  and  in  many  excel- 
lent examples,  the  column  constituted  the  whole  Order.  First  among  the  distinguishing 
features  was  the  ratio  of  the  height  of  the  shaft  to  its  diameter,  or  vice  versa.  To  find  the 
height  of  the  shaft,  or  the  size  of  any  member,  it  was  first  necessary  to  know  the 
diameter,  hence  the  practice  of  making  the  diameter  of  the  shaft  the  basis  of  all  calcula- 
tions in  architecture.  And  it  seems  that  so  long  as  this  practice  was  strictly  followed, 
architecture  improved,  natural  and  beautiful  forms  were  blended,  so  as  to  produce 
capitals  and  ornaments  in  some  of  the  Orders  that  challenge  the  admiration  of  all  men. 
while  the  proportions  of  some  examples  of  the  ancient  Orders  approximate  perfection. 
The  perfection  to  which  the  ancient  Orders  attained  was  not  due  to  the  efforts  or 
inventions  of  any  one  man,  but  to  the  combined  efforts  of  men  of  different  genera- 
tions, each    striving  to  carry  the  Order  to  a  higher  degree  of  perfection. 


8 


sxyvd  cs  -   


ARCHITECTURAL  PROPORTION. 


9 


Full  credence  must  not  be  given  to  stories  claiming  that  the  best  specimens  of 
the  old  Orders  were  the  first  given,  since  this  is  not  the  truth.  Nor  do  we  give 
more  credence  to  what  is  related  concerning  the  accomplishments  of  the  ancient 
architects,  for  it  seems  unreasonable  to  say  that  an  architect  could  learn  more  of 
each  art  and  science,  than  a  man  who  gave  his  whole  time  to  the  study  of  any 
one  in  particular,  yet  we  know  some  of  the  ancient  architects  wrote  on  all  the 
sciences.  Pythius,  Architect  of  the  Temple  of  Minerva,  at  Priene,  says:  "An 
architect  should  have  that  perfect  knowledge  of  each  art  and  science,  which  is 
not  even  acquired  by  the  professors  in  any  one  in  particular,  who  have  had  every 
opportunity  of  improving  themselves  in  it."  It  should  be  the  pride  of  every  honest 
and  unselfish  architect  to  so  construct  his  buildings  that  others  who  follow  the 
profession  after  his  time,  may  copy  or   improve  upon  his  inventions. 

Architects  who  expect  to  succeed  in  their  profession,  must  work  from  a  principle 
when  working  out  their  designs.  Buildings  designed  so  that  the  size  of  each 
member  is  governed  by  the  number  of  minutes  contained  in  the  corresponding 
member  on  the  standard  of  proportion  used,  will  always  be  worth  something  as  a 
work  of  art,  for  they  are  the  embodiment  of  a  principle  which  is  manifest  in  every 
detail,  and  like  an  imperfect  machine,  the  standard  may  be  improved  until  it  ap- 
proximates perfection.  Should  an  architect  wish  to  introduce  new  ratios  between 
the  members  of  his  work,  he  must  first  apply  them  to  an  Order,  or  a  Standard  of 
Proportion,  then  if  they  are  found  to  produce  well  balanced  and  suitable  members 
for  a  column,  and  are  applicable  to  the  interior  and  exterior  finish  of  a  building 
designed  to  fulfill  the  present  purposes  of  architecture,  his  system  will  be  com- 
pleted. But  to  give  heights  to  the  members  of  the  finish  for  the  interior  of  the 
building,  which  could  not  with  propriety  be  given  to  the  members  of  a  column 
equal  in  height  to  the  clear  height  of  the  room  or  story,  is  wrong,  because  the 
purposes  of  architecture  at  the  present  time  require  an  equality  of  ratios  between 
the  members  of  the  interior  and  exterior  work. 

A  standard  of  proportion  is  as  essential  to  a  building  of  any  kind,  as  it  is  to 
know  the  diameter  of  the  shaft  before  computing  the  size  of  the  members  of  a 
column.  Architects  who  use  their  eye  for  their  standard  of  proportion  are  never 
able  to  defend  their  work  in  a  contest,  for  they  have  no  principle  or  system  in  their 
designs. 

Many  writers  attempt  to  convey  the  idea  that  all  examples  of  any  of  the  Five  Orders 
were  alike,  but  such  teachings  are  not  founded  upon  truth.     It  is  right  and  proper  for 


ARCHITECTURAL  PROPORTION. 


10 


any  man  to  select  what  lie  thinks  is  the  best  example  of  any  given  Order,  and  praise  it 
as  much  as  he  chooses,  but  it  is  not  right  for  him  to  give  his  example  to  the  public  as 
the  Order,  when  he  knows  that  nearly  all  other  examples  of  the  Order  differ  from  the  one 
which  he  has  selected. 

We  are  willing  to  accord  to  the  architects  of  ancient  times  the  very  highest 
degree  of  intelligence,  but  are  not  prepared  to  believe  one-half  of  the  bosh  that  has  been 
Avritten  about  every  crooked  wall,  deformed  arch,  or  other  imperfection  found  in  any  ancient 
temple,  being  put  in  for  effect,  and  due  to  the  superior  intelligence  of  the  architect,  for 
if  it  is,  or  ever  was,  necessary  to  deform  an  object  or  body  in  order  to  make  it  look  well, 
few  sensible  men  will  follow  the  example. 

As  the  temples  of  the  ancients  cannot  be  copied  for  present  use,  we  shall  now  direct 
our  attention  to  a  standard  of  proportion  which  is  intended  to  apply  to  a  cheaper  class 
of  buildings,  better  suited  to  the  wants  of  the  American  people,  and  the  purposes  of 
architecture  in  this  country. 

To  clearly  show  the  necessity  for  a  standard  of  proportion  we  have  introduced  the 
column  shown  in  Plate  I.  As  a  standard  of  proportion  it  is  applicable  to  all  classes 
of  buildings.  The  diameter  of  the  shaft  above  the  base  is  divided  into  60  minutes  or 
units  of  measure.  The  taper  of  the  shaft  is  one-sixth  of  one  diameter,  or  50  minutes 
in  diameter  at  the  neck  below  the  fillet  and  astragal.  The  height  of  the  principal 
members  are:  Pedestal  base,  50  minutes;  die,  85  minutes;  cornice,  50  minutes;  shaft  base, 
36  minutes;  shaft,  including  base  and  capital,  10  diameters;  capital,  above  the  fillet  and 
astragal,  1  diameter  and  10  minutes;  architrave,  45  minutes;  frieze,  40  minutes;  cornice,  80 
minutes — whole  height  of  the  column  or  ' Order,  15^  diameters.  Referring  to  Plate  l  it  will 
be  seen  that  the  three  major  divisions  of  the  column  are  so  arranged  that,  for  vertical  pro- 
portion, they  are  applicable  to  the  three  major  divisions  of  the  elevation  of  an  interior  wall, 
and  vice  versa.  First:  The  height  of  the  pedestal  is  equal  to  the  distance  from  the  floor 
line  to  the  top  of  the  window-stool;  Second:  The  whole  height  of  the  shaft  equals  the 
height  of  the  perpendicular  architrave  for  the  window,  or  the  distance  from  the  top  of 
the  window-stool  to  the  soffit  or  lowest  edge  of  the  horizontal  architrave;  Third:  The 
height  of  the  entablature  is  equal  to  the  distance  from  the  sollit  to  the  ceiling  line. 

Of  the  minor  divisions  of  the  column,  the  pedestal  base  gives  the  proper  height  for 
the  room  base,  the  height  of  the  window-stool  or  sill  equals  the  height  of  the  pedestal 
cornice,  and  the  height  of  the  architrave  or  lowest  division  of  the  entablature  governs 
the  width  of  the  window  architrave. 

Each  member  or  part  of  the  interior  finish  contains  the  same  number  of  minutes  or  units 


II 


ARCHITECTURAL  PROPORTION. 


12 


of  measure  as  is  given  to  the  corresponding  member  on  the  column.  This  system  of 
proportion  gives  perfect  harmony  between  the  interior  and  exterior  finish,  is  easity 
understood  and  applied,  and  has  but  one  basis  from  which  the  size  of  any  part  or 
member  of  the  building  is  computed.  No  amount  of  decoration  can  hide  the  vulgar 
appearance  of  a  room  if  the  window  openings  show  a  greater  or  less  height  than  the 
corresponding  part  of  the  column  from  which  the  height  of  all  members  of  the  interior 
finish  is  computed.  The  room  base,  die  and  window-stool  of  any  room  represent  the 
three  divisions  of  the  pedestal  of  a  column  as  clearly  on  the  elevation  of  the  interior 
wall  as  the  same  members  do  on  a  pedestal  surmounted  hy  a  shaft  and  entablature. 
The  height  of  the  window  architrave  must  represent  the  height  of  the  shaft  of  the  Order, 
because  it  rests  upon  the  pedestal  and  supports  the  horizontal  architrave  or  lowest 
division  of  the  entablature.  To  complete  the  Order  on  the  interior  wall  elevation, 
the  stucco  cornice  must  contain  as  many  minutes  in  height  and  projection  as  given  to 
the  height  and  projection  of  the  cornice  or  upper  division  of  the  entablature  on  the 
standard  of  proportion. 

We  dismiss,  for  the  present,  Architectural  Proportion,  and  take  up  a  subject  equally 
important  and  often  criminally  neglected: 

FOUNDATIONS. 

A  good  foundation  is  the  key  to  success  in  everything,  and  without  it  a  fine 
house  is  only  a  costly  sham.  When  the  walls  and  plaster  of  a  new  building  begin  to 
crack,  it.  is  usually  charged  to  climatic  influences,  }^et,  in  nearly  every  case,  the  cause 
can  be  traced  directly  to  a  faulty  foundation.  Good  walls,  with  broad  footings  of  stone 
or  hard-burned  brick,  will  always  give  the  owner  of  a  building  better  satisfaction  than 
he  can  receive  from  a  hundred  theories  that  work  well  only  on  paper. 

To  insure  a  good  foundation  all  walls  should  start  from  a  common  level,  either  at 
the  bottom  of  the  basement,  or,  if  no  basement  is  required,  then  in  trenches  excavated 
to  a  sufficient  depth  to  insure  equal  resistance  from  the  ground.  A  good  foundation  at 
one  place  is  often  an  insufficient  one  for  the  same  building  even  on  an  adjoining  lot. 
Therefore,  it  is  always  advisable  for  the  architect  to  visit  the  building  site  after  the 
excavating  is  done,  when  he  will  readily  detect  any  great  inequality  in  the  density  of 
the  earth  along  the  line  of  the  walls,  and  will  then  be  competent  to  make  a  suitable 
foundation  for  that  particular  place.  The  width  of  foundation  and  basement  walls 
should  always  be  liberal  and  rather  more  than  appears,  after  examination  of  the  under- 


ARCHITECTURAL  PROPORTION. 


13 


lying  earth,  to  be  necessary.  If  extravagance  can  be  justified  at  all  in  the  erection  of 
a  building,  the  foundation  should  have  the  lion's  share;  and  he  who  cannot  afford  to 
build  upon  a  good  foundation  will  soon  regret  having  built  at  all,  for  upon  the  solidity 
of  the  foundation  depends  the  lasting  beauty,  usefulness,  and  safety  of  the  whole 
superstructure. 

As  the  safety  of  the  whole  superstructure  depends  upon  the  solidity,  so  also  does  the 
exterior  appearance  of  an  isolated  building  depend,  in  a  large  degree,  upon  the  height 
of  the  foundation. 

A  two  or  three  story  dwelling  with  the  first-floor  line  only  one  and  a  half  or  two 
feet  above  the  level  of  the  ground,  presents  the  appearance  of  having  settled  after  com- 
pletion ;  and  a  low  building  with  a  very  high  foundation  has  the  appearance  of  having 
been  raised  above  high  water  mark.  In  either  case  the  architect  who  designs  such 
buildings  usually  makes  them  bear  false  witness  against  the  locality  wherein  they  are 
erected. 

As  an  illustration  of  Rule  I,  we  will  refer  the  reader  to  the  section  of  the  eleva- 
tion of  a  cottage  and  foundation  shown  in  Plate  I.  The  clear  height  of  the  story  in 
the  cottage  is  10  feet,  or  equal  to  the  height  of  the  column  shaft  shown  in  the  same 
Plate,  and  as  the  diameter  of  the  shaft  is  the  basis  from  which  the  height  and  projec- 
tion of  the  members  of  the  column  is  computed,  we  take  the  height  of  the  story  as  the 
representative  of  the  shaft;  and  divide  this  height  into  10  diameters  and  then  divide  one 
diameter  into  60  parts  for  the  unit  of  measure  which,  in  this  case,  equals  y"u  or  \  of 
an  inch.  Proceeding  then  as  with  a  column,  the  height  of  the  foundation  to  the  floor 
line  is  made  to  equal  2  diameters  and  45  minutes,  or  2  feet  9  inches.  The  height  of  the 
stone  base  to  the  foundation  is  made  to  equal  50  minutes  or  10  inches,  and  the  height  of 
the  water-table  equals  30  minutes  or  6  inches. 

Then  beginning  at  the  ceiling  line  2  diameters  and  45  minutes,  or  2  feet  9  inches 
is  laid  up  for  the  height  of  the  entablature,  or  the  distance  from  the  ceiling  line  to 
the  eaves. 

As  the  cornice  on  the  standard  is  80  minutes  in  height  and  projection,  the  height 
of  the  cottage  cornice  measured  at  right  angles  from  the  slant  of  the  roof,  and  the 
inclined  and  end  projection  is  made  to  equal  80  minutes,  or  1  foot  4  inches. 

The  members  of  the  cornice  on  the  dwelling  contain  the  same  number  of  minutes, 
or  units  of  measure,  as  is  given  to  the  corresponding  member  of  the  cornice  on  the 
standard,  with  this  exception:  one  member  is  left  out  of  the  corona  in  the  cottage 
cornice,  and  its  height  is  added  to  the  height  of  the  bed  mould  in  order  to  give  that 


BASE  or  SHAFT. 


ARCHITECTURAL  PROPORTION. 


15 


member  more  prominence  in  its  retired  position  in  the  raking  cornice,  and  the'  height 
of  the  dental  course  and  spiral  mould  next  below  are  both  given  to  the  lowest  division 
of  the  plain  cornice. 

Plate  I  also  represents  the  standard  of  proportion  as  standing  in  a  room,  the  clear 
height  of  which  equals  15  feet  6  inches.  Then  in  order  to  keep  the  same  ratios  between 
the  members  of  the  interior  story  finish  of  the  cottage  and  the  members  of  the  column, 
it  becomes  necessary  to  reduce  the  standard  of  proportion,  until  it  will  stand  in  a 
room  or  story  which  is  only  LO  feet  in  height.  This  we  do  by  reducing  10  feet  to 
hundredths  or  thousandths  of  inches  and  dividing  by  15§.  The  quotient  resulting  there- 
from will  be  the  diameter  of  the  shaft  of  the  reduced  column. 

The  sum  obtained  for  the  diameter  is  then  subdivided  into  60  minutes,  and  one 
minute,  or  the  unit  of  measure  thus  found  for  the  10-foot  story,  is  increased  as  many 
times  for  the  height  of  each  member  of  the  story  finish  as  there  are  minutes  in  the 
height  of  the  corresponding  member  on  the  standard  example.  120.000  inches  15^  = 
7tVo  inches  for  the  diameter  of  the  shaft  of  the  reduced  column.  7.740  -s-  GO  =  iW'o 
inches  for  the  unit  of  measure  for  the  10-foot  story.  .129X50— 6rVo  inches  for  the 
height  of  the  room  base  for  the  cottage.  .129X30=3tV(7  inches  for  the  height  of  the 
window-stool  and  sill.  7.74X  10  -llxsn  inches,  or  G  feet  5,W  inches  for  the  height  of 
the  window  architrave,  or  the  distance  from  the  top  of  the  window-stool  to  the  soffit 
above  the  window.  .I29X45X5^nj  inches  for  the  width  of  the  window  arhictraves. 
.129X80=10i:!</i7  inches  for  the  height  and  projection  of  the  stucco  cornice  in  the  cottage 
or  any  story  which  has  a,  height  of  just  10  feet. 

It  will  be  seen  that  the  members  on  the  interior  elevation  of  the  room  contain 
exactly  as  many  parts  or  minutes  in  height  as  is  given  to  the  corresponding  members 
on  the  standard,  and  that  there  is  a  perfect  equality  of  ratios  between  the  members  of 
the  exterior  and  interior  work. 

In  Plata,  I  is  also  shown  the  elevation  of  the  veranda  post,  balustrade,  and  part 
elevation  of  the  cornice.  As  the  whole  height  from  tin.'  floor  line  to  the  top  of  the 
cornice  is  10  feet,  the  denomination  of  the  unit  of  measure  for  the  verandah  finish  is 
iWo  inches,  or  the  same  as  for  the  interior  story.  Commencing  at  the  floor  line  of 
the  verandah,  the  plinth,  or  plain  part  of  the  pedestal  base  is  33  minutes  in  height, 
as  on  the  standard,  and  the  moulded  part  17  minutes  in  height,  making  the  whole 
height  of  the  base  equal  50  minutes.  .1 20X33  -=4, %*a  inches.  .129X1  7=2  iW  inches. 
.129X85=1  OA6*  inches  for  the  height  of  the  pedestal  die.  .129X30=3i<&  inches  for 
the  height  of  the  pedestal  cornice.     7.74X10=6  feet  5iV»  inches  for  the  height  of  the 


1G 


PLATE  V. 


ARCHITECTURAL  PROPORTION. 


17 


post  above  the  pedestal.  .  129X45=5 nor  inches  for  the  diameter  of  the  post.  Eighty- 
five  minutes — the  height  of  the  architrave  and  frieze  on  the  standard — multiplied  by 
.129=10.965  inches  for  the  height  of  the  bracket,  spandrel,  or  other  finish,  between  the 
top  of  the  post  and  the  lowest  line  of  the  cornice.  .129X80=10iVV  inches  for  the 
height  and  projection  of  the  verandah  cornice. 

Inasmuch  as  the  diameter  of  the  post  equals  I  of  the  diameter  of  a  round  shaft  of 
the  same  length,  to  find  the  projection  of  the  die  and  other  members  from  the  center 
of  the  post,  the  unit  of  measure  is  multiplied  by  \  of  the  number  of  parts  given  for  the 
projection  of  the  members  of  the  pedestal  of  the  standard. 

Plate  II  shows  a  section  of  the  window-stool  and  architrave  for  the  window  shown 
in  Plate  I.  for  a  story  15  feet  6  inches  clear.  The  length  of  the  architrave  or  casing 
is  10  feet  and  its  width  9  inches,  or  45  parts  of  one  diameter.  The  principal  members 
of  the  side  architraves  for  the  openings  contain  the  same  number  of  parts  as  is  given 
to  the  members  of  the  entablature  architrave  shown  in  Plate  IX.  Two  members  are 
added  to  the  lowest  part,  or  inner  edge  of  the  architraves  for  the  windows  and  doors,  in 
order  to  break  up  the  plain  surface  of  that  part  of  the  architrave  which  is  covered  by 
a  wreath  in  the  entablature. 

Plate  III  shows  a  section  of  the  room  base  with  the  height  of  each  member  given. 
The  drawings  are  merely  intended  to  illustrate  the  rules  and  show  the  number  of  parts 
that  are  given  to  each  member.  The  form  of  the  members  for  the  story  finish  can 
be  varied  to  suit  the  fancy  of  the  designer. 

Plate  IV  shows  the  shaft  base  and  the  height  and  projection  of  each  member  from 
the  center  of  the  shaft. 

Plate  V  shows  the  height  and  projection  of  the  members  of  the  pedestal  cornice 
and  the  projection  of  the  die  from  the  central  line.  The  height  and  projection  of  the 
members  of  the  capital  are  shown  in  Plate  VI,  and  require  no  explanation. 

The  cornice  or  upper  division  of  the  entablature,  is  shown  on  a  large  scale  in  Plate  VII. 
The  modillions  may  be  carved  and  ornamented,  or  left  plain,  as  the  style  of  the  work  requires. 

From  the  entablatures  of  street  fronts,  which  are  elevated  above  the  standard  of 
proportion,  it  is  not  necessary  to  exclude  any  of  the  minor  members,  for  the  denomina- 
tion of  the  unit  of  measure  will  be  increased  as  the  entablature  is  elevated,  consequently 
the  size  of  each  member  will  be  increased  in  its  proper  ratio;  but  from  entablatures 
for  any  part  of  a  building  where  the  denomination  of  the  unit  of  measure  is  decreased, 
as  the  elevation  is  increased  above  the  first  floor  line,  the  minor  members  should  be 
excluded,  and  the  principal  ones  enlarged. 


CAPITAL 


ARCHITECTURAL   PROPORTION.  19 


A  facade  with  portico,  and  window  and  door  entablatures  in  any  Order,  and  having  a  sim- 
ple cornice  at  the  greatest  elevation,  is  the  reverse  of  good  taste,  or  any  rule  in  archi- 
tecture; but  entablatures  for  the  building  and  portico  may  be  used  with  good  effect,  when 
there  are  no  entablatures,  or  even  projecting  architraves  on  the  window  and  door  openings. 

It  is  hardly  proper  to  support  a  portico  entablature  with  square  posts,  or  to  place 
a  cornice  without  frieze  or  architrave,  above  the  round'  shafts  of  any  Order;  but  pilasters 
projected  one-half  the  width  of  their  face  from  the  wall,  and  having  capitals,  may  be 
properly  set  under  the  entablatures  of  street  fronts  or  other  facades. 

The  proper  divisions  of  a  simple  cornice  are  represented  in  Plate  Till,  also  the  pro- 
jection of  the  members  from  the  face  of  the  wall.  In  all  Plates  showing  parts  of  the 
finish  or  members  of  the  column,  the  figures  give  the  projection  of  the  members  from 
the  center  of  the  shaft,  or  what  is  usually  called  the  axis  of  the  column. 

The  principal  members  of  the  cornices  shown  in  Plates  VII  and  VIII,  contain  the 
same  number  of  minutes  in  height;  and  the  projection  of  the  square  of  the  cymatium 
in  Plate  VII  from  the  face  of  the  frieze,  is  equal  to  the  projection  of  the  corresponding 
member  in  Plate  VIII  from  the  wall  line,  which  would  be  the  face  of  the  frieze  in  an 
entablature. 

Plate  IX  represents  a  large  scale  drawing  of  the  architrave,  or  lowest  division  of  the 
entablature  of  the  standard  of  proportion  shown  in  Plate  I.  The  form  of  the  lowest 
member  is  well  adapted  to  the  proper  shading  of  vine  or  wreath  ornaments,  projected 
sufficiently  from  the  retired  face  of  the  member  to  give  the  leaves  a  natural  and  varied 
appearance,  but  for  ordinary  work  this  member  may  be  left  without  ornamentation. 

Plate  X  with  the  explanations,  fully  illustrates  our  system  of  reducing  superimposed 
stories.  We  are  aware  that  this  is  a  grave  departure  from  the  rules  and  usages  of  many 
architects,  and  that  it  does  not  at  all  conform  to  the  Alisma  Plantayo  example,  if  the 
eminent  art  critic  who  made  use  of  that  illustration  intended  it  to  apply  to  super- 
imposed stories,  for  the  system  which  Plate  X  illustrates,  does  not  reduce  the  superim- 
posed stories  so  much,  and  particularly  the  third  and  fourth  ones  shown   in  the  section. 

Examples  of  lateral  or  vertical  proportion  taken  from  old  palaces  or  churches,  built 
hundreds  of  years  ago,  may  be  interesting  as  a  study,  but  they  have  no  practical  value 
in  the  architecture  of  this  country. 

From  an  author  and  architect  of  the  present  day,  we  have  an  example  now  before 
us  in  which  each  superimposed  story  is  just  two  feet  less  in  height  than  the  one  next 
below.  This  system  reduces  the  superimposed  stories  so  fast  that  the  fourth- story 
windows  appear  to  be  almost  square. 


20 


ARCHITECTURAL  PROPORTION. 


21 


It  must  be  remembered  that  feet  and  inches  are  not  the  units  of  measure  in  archi- 
tecture, and  that  all  heights  and  widths  should  first  be  found  in  diameters  and  minutes, 
and  the  height  of  superimposed  stories  by  the  multiplication  or  division  of  the  unit  of 
measure  used  for  the  first  story.  After  a  measure  has  been  determined  in  the  proper  way, 
it  may  be  reduced  to  feet  or  inches,  and  used  as  such,  but  not  before,  without  confusion. 

The  system  which  we  here  introduce  for  finding  the  height  of  superimposed  stories 
is  to  make  the  unit  of  measure  used  for  the  second  story  equal  seven-eighths  of  the  unit  used 
for  the  first  story;  and  the  unit  for  the  third  story  to  equal  seven-eighths  of  the  unit  of  the 
second;  the  unit  for  the  fourth  story  seven-eighths  of  the  unit  of  the  third;  and  so  on 
through  all  of  the  stories.  Then  the  proportion  is:  As  the  height  of  the  first  is  to  the 
height  of  the  second,  so  is  the  height  of  the  third  to  the  height  of  the  fourth.  Each  hori- 
zontal space  of  dead  wall  between  the  openings  is  diminished  in  the  same  ratio;  also  the 
height  of  each  superimposed  opening  and  the  finish  thereof,  and  the  height  of  all 
interior  story  finish. 

In  Plate  X  an  outline  sketch  of  the  standard  of  proportion  is  shown  in  each  story. 
As  the  first  story  is  15  feet  G  inches  clear  —  the  whole  height"  of  the  standard  of 
proportion — the  diameter  for  that  story  is  one  foot,  and  the  unit  of  measure  is  nra  inches. 
We  will  give  one  series  of  explanations,  and  show  the  application  of  the  rules  to  each 
story  and  the  finish  thereof.  (See  Rules  VI,  VII,  VIII.)  For  the  base  of  the  first  story, 
we  multiply  the  unit  of  the  measure  by  the  number  of  minutes  contained  in  the  height 
of  the  pedestal  base  of  the  standard  of  proportion  (see  Rule  IX),  .20X50  =  10  inches  for 
the  height  of  the  room  b  ase,  including  the  mould.  Rule  X — .20X33 — Gi'i/V  inches  for 
the  base  plinth,  leaving  3i4A  inches  for  the  height  of  the  moulded  part.  Rule  XI — 
.20X30=6  inches  for  the  height  of  the  window-stool  and  sill.  Rule  XII—  12X10=120 
inches,  or  10  feet,  for  the  height  of  the  interior  window  architrave,  or  the  distance 
from  the  top  of  the  window-stool  to  the  soffit  above  the  window.  Rule  XIII — .20X45= 
9  inches,  for  the  width  of  the  window  architrave.  Rule  XIV — .20X80=10  inches,  for 
the  height  and  projection  of  the  stucco  cornice  in  the  first  story.  Rule  XV  gives  iVW 
inches  for  the  unit  of  measure  for  the  second  story.  Rule  XVI — .175X60=10iV°<r  inches 
for  the  diameter.  Rule  XVII— 10.50X"!  5|  =  13  feet  CW  inches  for  the  clear  height  of 
the  second  story.  Again  applying  the  rules  for  finding  the  height  and  width  of  the 
story  finish,  we  get  8i7„V  inches  for  the  height  of  the  room-base  in  the  second  story,  for 
the  window-stool  and  sill,  orA  inches,  window  architrave,  8  feet  9  inches  in  height,  and 
7iVo  inches  in  width,  and  1  foot  2  inches  for  the  height  and  projection  of  the  stucco 
cornice.    After  reducing  iVu'V  inches  in  accordance  with  Rule  XV,  we  get  iWu  inches  for 


zz 


ARCHITECTURAL  PROPORTION. 


23 


the  unit  of  measure.  inches  for  the  diameter,  and  1  I  feet  lOiav  inches  for  the  clear 

height  of  the  third  story.  Applying  the  rules  as  before,  the  height  of  the  room  base 
is  7/W  inches,  window-stool  and  sill,  4i'Vlo  inches,  window  architrave,  7  feet  7i8o°o  inches  in 
height,  and  6itot  inches  in  width,  and  the  height  and  projection  of  the  stucco  cornice  for 
the  third  story  12 nfo  inches.  For  the  fourth  story  the  unit  is  nn/u  inches,  diameter  Svh 
inches,  and  the  clear  height  10  feet  4r,A  inches.  Height  of  base,  61V0  inches,  window- 
stool  and  sill,  4i°o2o  inches,  length  or  height  of  window  architrave,  G  feet  8iW  inches,  and 
width  Gi'o'V  inches,  height  and  projection  of  the  stucco  cornice  in  the  fourth  story, 
IOiVtt  inches. 

The  depth  of  the  beams  including  floor  and  plaster,  is  equal  to  80  units  of  the  story 
below  them,  but  their  depth  will,  of  course,  always  depend  upon  the  width  of  the  span, 
and  the  safe  load  they  are  intended  to  carry.  The  interior  elevation  of  each  story 
presents  the  outline  of  a  complete  Order,  as  shown  in  the  following  comparative  table: 


COLUMX.  Parts.                                     STORY.  Fasts. 

Height  of  Pedestal  Base  50  Height  of  Room  Base  50 

"     "  .     "       Die  85  "  "     "     Die  85 

"      "       "       Cornice  30  "  "  Window-Stool,  30 

"      "  Shaft,  10  dia.  "  »  Window  Casing,  10  dia. 

"      "  Architrave,  45  "  "  Window  Architrave,  45 

:'      "  Frieze  40  "  "  Frieze  40 

"      "  Cornice  80  "  "  Stucco  Cornice  80 


Whole  height,  15^  dia.  Whole  height,  15^  dia. 

Many  devices  have  been  resorted  to  by  authors  for  finding  the  height  of  entablatures 
or  cornices  which  are  elevated  above  their  standard  of  proportion,  but  all  are  more  or  less 
complicated;  and  a  great  many  of  them  amount  to  nothing  more  than  an  intelligent 
guess.  The  system  which  we  will  now  introduce  is  very  simple  and  probably  has  as 
many  claims  to  excellence  as  the  best  that  are  in  use. 

The  lowest  line  of  the  entablatur  e  on  the  standard  of  proportion  which  we  have 
introduced  for  this  work  is  12  feet  9  inches  above  the  floor  line.  Up  to  that  eleva- 
tion the  height  of  portico  or  wall  entablatures  is  found  by  dividing  the  distance  they 
are  elevated  above  the  floor  line  by  12£— the  number  of  diameters  contained  in  the  com- 
bined height  of  the  pedestal  and  shaft;  and  then  by  multiplying  the  quotient  by  2| — the 
number  of  diameters  contained  in  the  height  of  the  entablature. 

By  referring  to  the  tables  where  ,'„"„  inches  is  the   unit  of  measure,  it  will  be  seen 


24 


ARCHITECTURAL  PROPORTION. 


25 


that  the  distance  from  the  floor  line  to  the  entablature  is  12  feet  li'Vo  inches,  or  7 1 (j I o 
inches  less  than  the  height  just  given  from  the  standard  of  proportion.  Then,  as  the 
addition  of  tso  inches  to  the  unit  of  measure  increases  the  combined  height  of  the 
pedestal  and  shaft,  Ti'oV  inches,  it  seems  that  the  most  reasonable  way  to  reduce  entab- 
latures below  what  an  Order  would  make  them,  if  continued  to  an  indefinite  height, 
would  be  to  increase  the  distance  between  the  minutes,  that  is,  make  the  distance 
between  tVo  inches  and  xW  inches  a  little  more  than  Tt'o'u  inches — the  distance  between 
tuts  inches  and  j0°u  inches;  and  continue  that  increase  in  regular  ratios  indefinitely. 

The  following  table  gives  the  proper  elevation  at  which  the  different  units  from  tsjs 
inches  to  toV  inches  are  used;  also  the  height  of  the  entablature  at  each  point  or  eleva- 
tion, and  the  projection  from  the  face  of  the  frieze.  This  table  was  calculated  in  the 
manner  above  explained,  and  we  leave  it  to  others  in  practice  to  make  the  distance 
between  the  points  where  the  different  units  are  used  greater  or  less,  as  the  style  of 
their  work  requires. 


ARCHITECTURAL  PROPORTION. 


27 


TABLE  SHOWING  THE  HEIGHT  AND  PROJECTION  OF  ENTABLATURES  WHICH  ARE 
ELEVATED  ABOVE  THE  STANDARD  OF  PROPORTION. 


CD 
> 

a  © 

> 

h 

tion  abo 
or  Line. 

DO 

se 
l3 
M 

o  g 

.SP  ^ 
5  j* 

ction  fro 
of  Friez 

tion  abo 
or  Line. 

BD 

<«  £ 

O  g 
"to  ^~ 

p  S 

£i  .« 
o  ^ 

a  o 

o 

W  s 

03  jo 

"o 

W  a 

w 

'c 
P 

w 

Ph  £ 

3 

13:4.70 

o- 1  n  ak 

1:4.80 

27:7.50 

.Of 

K.  1  A£ 

o:  1.U5 

O.  rt  cm 

z:  o.bU 

14:0.50 

oo 
.22 

o.  U.oU 

1:5.60 

28:11.70 

QQ 
.OO 

5:  Z.  /U 

I.  U.4U 

14:8.45 

o.  i.yo 

1:6.40 

30:4.85 

QQ 

.oU 

y:  4.oo 

O.  7  OA 

z:  /  .ZU 

±o.t  .UU 

O  f 

o.  O.UU 

1  .  1  OA 

01.11  flA 

61: 11. UO 

/i  a 
.4U 

k.  f1  aa 
o:  U.UU 

0.  Q  AA 

1.  O.UU 

16:1.00 

<J.  O.  ZO 

1:8.00 

33:6.20 

.41 

o:  <.65 

O.  Q  QA 

/:  o.oU 

16:9.70 

.26 

3:6.90 

1:8.80 

35:2.50 

.42 

5:9.30 

2:9.60 

17:6.75 

.27 

3:8.55 

1:9.60 

36:11.95 

.43 

5:10.95 

2:10.40 

18:4.20 

.28 

3:10.20 

1:10.40 

38:10.60 

.44 

6:0.60 

2:11.20 

19:2.10 

.29 

3:11:85 

1:11.20 

40:10.50 

.45 

6:2.25 

3:0.00 

20:0.50 

.30 

4:1.50 

2:0.00 

42 :11.70 

.46 

6:3.90 

3:0.80 

20:1.1.45 

.31 

4:3.15 

•  2:0.80 

45:2.25 

.47 

6:5.55 

3:1.60 

21:11.00 

.32 

4:4-80 

2:1.60 

47:6.20 

.48 

6:7.20 

3:2.40 

22:11.20 

.33 

4:6.45 

2:2.40 

49:11.60 

.49 

6:8.85 

3:3.20 

24:0.10 

.34 

4:8.10 

2:3.20 

52:6.50 

.50 

6:10.50 

3:4.00 

25:1.75 

.35 

4:9.75 

2: 4 .00 

55:2.95 

.51 

7:0.15 

3:4.80 

26:4.20 

.36 

4:11.40 

2:4.80 

58:1.00 

.52 

7:1.80 

3:5.60 

ARCHITECTURAL  PROPORTION. 


28 


RULES. 


Rule  I. — To  find  the  height  of  foundation  for  a  one-story  isolated  building:  divide 
the  clear  height  of  the  story  into  10  diameters,  and  make  the  height  of  the  foundation  to 
the  floor  line  equal  2f  diameters. 

Rule  II. — To  find  the  distance  from  the  ceiling  line  of  a  one-stoiw  building  to  the 
lowest  line  of  the  eaves:  divide  the  clear  height  of  the  story  into  10  diameters,  and 
make  the  distance  from  the  ceiling  line  to  the  eaves  equal  2f  diameters. 

Rule  III. — To  find  the  height  and  projection  of  the  cornice  for  a  one-story  building: 
divide  the  clear  height  of  the  story  into  10  diameters,  and  make  the  height  and  pro- 
jection of  the  cornice  equal  1^  diameters,  or  80  minutes. 

Rule  IV.— To  find  the  height  of  the  stone  base  for  a  foundation:  divide  one 
diameter  into  GO  minutes,  and  make  the  height  of  the  base  equal  50  minutes. 

Rule  Y. — To  find  the  height  of  the  water-table:  divide  one  diameter  into  CO  minutes, 
and  make  the  height  of  the  water  table  equal  30  minutes. 

Rule  VI. — To  find  the  diameter  of  the  shaft  when  the  whole  height  of  the  column 
(pedestal,  shaft  and  entablature)  is  given:  divide  the  height  by  15^. 

Rule  VII. — To  find  the  proper  diameter  of  any  story:  divide  the  clear  height  of  the 
story  by  1 5^. 

Rule  VIII. — To  find  the  unit  of  measure  for  any  story:   divide  the  diameter  by  60. 

Rule  IX. — To  find  the  whole  height  of  t lie  room-base  for  any  story:  multiply  the 
unit  of  measure  by  50. 

Rule  X. —  To  find  the  height  of  the  plinth,  or  plain  part  of  the  room-base:  multiply 
the  unit  of  measure  by  33. 

Rule  XI. — To  find  the  height  of  the  window-stool,  or  sill,  for  an)'  story:  multiply 
the  unit  of  measure  by  30. 

Rule  XII. — To  find  the  height  of  the  interior  window  casing  or  architrave  for  any 
story:  multipl}7  the  diameter  of  the  story  by  10. 

Rule  XIII.— To  find  the  width  of  the  window-architrave  for  any  story:  multiply 
the  unit  of  measure  by  45. 


4 


ARCHITECTURAL  PROPORTION. 


29 


Rule  XIV. — To  find  the  height  and  projection  of  the  stucco  cornice  for  any  story: 
multiply  the  unit  of  measure  by  .80. 

Rule  XV. — To  find  the  unit  of  measure  for  any  superimposed  story:  take  ^  of  the 
unit  used  for  the  story  next  below. 

Rule  XVI. — To  find  the  diameter  of  any  superimposed  story:  multiply  the  unit  of 
measure  by  60. 

Rule  XVII. — To  find  the  clear  height  of  any  superimposed  story:  multiply  the 
diameter  by  15^. 

Rule  XVIII. — To  find  the  width  of  any  door  or  window  architrave,  or  the  diameter 
of  a  post:  divide  the  height  into  10  diameters  and  make  the  width  equal  45  minutes, 
or  |  of  one  diameter. 

Rule  XIX. — To  find  the  width  of  a  pilaster:  divide  the  height  into  10  diameters, 
and  make  the  width  equal  50  minutes,  or  £  of  one  diameter. 

Rule  XX. — To  find  the  width  of  an}'  single  door  or  window:  divide  the  height  into 
10  diameters,  and  make  the  width  equal  \\  diameters. 


ARCHITECTURAL  PROPORTION. 


30 


TABLE  OF  COLUMN  FINISH. 


i 

o 

oc 
3 
hI 

H 

8 1 
°» 

*  ~ 

£  -5 

5 

55 
=»- 
c 

<L 

5 

S. 

C 

c 
'a 

c 

a 
tr 

X 

n 

0 

QC 
0 

& 

"tc 

V 

$ 

k 

o 
m 

Si 
"t 

K 

Peclestiil  Cornice. 

S  o*S  • 

£  «  »2 
<C  ®  a  3 

83f! 
5  ■-  ~~. 

J.-2  || 

K  a 
W 

0 

Tc 

a 
"c 

9 

5: 0  00 

G. 

00 

5. 

00 

7. 

00 

3. 

60 

1:4. 

50 

5 

00 

3 

00 

6:4.50 

1:4 

50 

7:9.00 

.100 

5: 0 .  GO 

6. 

0G 

5. 

05 

7. 

07 

3. 

636 

1:4.665 

5. 

05 

3. 

03 

6: 5 . 265 

1:4 

665 

7:9. 

93 

.101 

5: 1 . 20 

6. 

12 

5 

10 

7. 

14 

3. 

672 

1:4.83 

5. 

10 

3. 

06 

6:6.03 

1:4 

83 

7:10  86 

102 

5: 1 .80 

6 

18 

5. 

15 

7. 

21 

3. 

708 

1:4.995 

5. 

15 

3. 

09 

6:6.795 

1:4 

995 

7:11 

.79 

.103 

5: 2 . 40 

6 

24 

5. 

20 

7. 

28 

3. 

744 

1:  5 . 

16 

5. 

20 

3 

12 

6: 7  56 

1:5 

16 

8:0.72 

.104 

5: 3 . 00 

6 

30 

5 . 

25 

7. 

35 

3. 

78 

1:5. 

325 

5. 

25 

3. 

15 

6:8.325 

1:5 

325 

8:1. 

65 

.105 

5: 3 . 00 

6 

36 

5 

30 

7. 

42 

3. 

816 

1:5. 

49 

5. 

30 

3. 

18 

6:9.09 

1:5 

49 

8:2. 

58 

.106 

5: 4 . 20 

6.42 

5. 

35 

7. 

49 

3. 

852 

1:5 

655 

5 

35 

3. 

21 

6:9.855 

1:5 

655 

8:3. 

51 

107 

5: 4 . 80 

6 

48 

5.40 

7. 

56 

3. 

888 

1:5 

82 

5 

40 

Q 
U  . 

24 

6: 10.62 

1:5 

82 

8:4 

44 

.108 

5: 5 . 40 

6 

54 

5 

45 

7. 

63 

3. 

924 

1:5.985 

5.45 

3. 

27 

6:11.385 

1:5 

985 

8:5. 

37 

.109 

5:  (i .  00 

6 

GO 

5 

50 

7 

70 

3 

96 

1:6 

15 

5. 

50 

3 

30 

7:0.15 

1:6 

15 

8:6 

30 

.110 

5: 6 . 60 

G 

66 

5 

55 

7 

77 

3.996 

1:6 

315 

5  55 

3 

33 

7: 0 . 915 

1:6 

315 

8:7 

23 

111 

5: 7 . 20 

6 

72 

5 

60 

7 

84 

4.032 

1:6.48 

5 

60 

3 

36 

7.T.68 

1:6 

48 

8:8 

16 

.112 

5: 7 . 80 

6 

78 

5 

65 

7 

91 

4.068 

1:6 

645 

5 

65 

3 

39 

7:2.445 

1:6 

645 

8:9 

09 

.113 

5: 8 . 40 

6 

84 

5 

70 

7 

98 

4 

104 

1:6 

81 

6 

70 

3.42 

7:3.21 

1:6 

81 

8:10.02 

114 

o»  V  .  \J\J 

G 

.90 

5 

75 

8.05 

4 

14 

1:6 

975 

5 

75 

3 

45 

7-3  07  R 

1:6 

.975 

8:10.95 

11 R 

5:9. GO 

G 

.96 

5 

80 

8 

12 

4 

176 

1:7 

14 

5 

80 

3 

48 

7:4.74 

1:7 

14 

8:11.88 

.116 

5:10.20 

7 

02 

5 

85 

8 

19 

4.212 

1:7 

305 

5 

85 

3 

51 

7: 5 . 505 

1:7 

.305 

9:0 

81 

.117 

5:10.80 

7 

.08 

5 

90 

8 

26 

4.248 

1:7 

.47 

5 

90 

3 

54 

7:6.27 

1:7 

.47 

9:1 

74 

.118 

5:11.40 

7 

14 

5 

95 

8 

33 

4.284 

1:7 

.625 

5 

.95 

o 
o 

57 

7:7  025 

1:7 

.625 

9:2 

67 

.119 

G:0.00 

7 

.20 

6 

00 

8 

40 

4.32 

1:7 

.80 

6 

.00 

3 

GO 

7:7.80 

1:7 

.80  jj 

9:3 

60 

120 

G:0.00 

7 

.26 

6 

05 

8 

47 

4  356 

1:7 

.965 

6 

.05 

3 

.63 

7:8.565 

1:7 

965 

9:4.53 

.121 

6:1  20 

7 

.32 

6 

.10 

8 

.54 

4.392 

1:8 

.13 

6 

10 

3 

.06 

7:9.33 

1:8 

.13 

9:5.46 

.  122 

6:1.80 

7 

.38 

6 

.15 

8 

.61 

4.428 

1:8 

.295 

6 

15 

o 
o 

.69 

7:10.095 

1:8 

.295 

9:6 

.39 

.123 

6: 2 . 40 

7 

.44 

6 

.20 

8 

.68 

4.4G4 

1:8 

.46 

6 

20 

3 

.72 

7:10.86 

1:8 

.46 

9:7 

32- 

124 

ARCHITECTURAL  PROPORTION. 


31 


TABLE  OF  COLUMX  FINISH.— Continued. 


^3  ■ 

si 


02  . 

C  O 


3 


7.50 
7.56 
7.62 
7.68 
7.74 
7.80 
7.86 

7  92 
7.98 
8.04 
8.10 
8.16 
8.22 
8.28 
8.34 
8.40 
8.4(5 
8.52 
8.58 
8.64 
8.70 
8.76 
8.82 
8.88 

8  94 
9.00 
9.06 
9.12 
!).  18 


6.25 
6.30 
6.35 
6  40 
6.45 
6.50 
6.55 
6.60 
6.65 
0 . 70 
0  75 
6  80 

6  85 
6.90 
6 . 95 
7.00 

7  05 
7.10 
7  15 
7  20 
7  25 
7 . 30 
7 . 35 
7.40 
7  45 
7.50 
7.55 
7.60 
7.65 


8.75 
8.82 
8.89 
8.06 
9.03 
9.10 
9.17 
9  24 
9.31 
9.38 
9.45 
9.52 
9 . 59 
9.61) 
9 . 73 
9.80 
9.87 
9  94 
10 . 01 
10  08 
10  15 
10.22 
10  29 
10  36 
10.43 
10.50 
10 . 57 
10  04 
10  71 


4.50 

4  536 
4.576 
4.608 
4.644 
4.68 
4.710 
4.752 
4.788 
4.824 
4.86 
4.896 
4.932 
4.968 
5.001 
5.04 

5  076 
5.112 
5 . 148 
5  ISt 
5  22 
5  256 
5  292 
5 . 328 
5.364 
5.40 
5.436 
5.472 
5  508 


a.  'ji 


x4 


1:8  625 

1:8  79 

1: 8 . 955 

1:9.12 

1:9.285 

1:9.45 

1:9.615 

1:9.78 

1:9.945 

1:10.11 

1:10  275 

1:10  44 

1:10  605 

1:10.77 

1:10.935 

1:  11  10 

1:11.265 

1:11.43 

1:11.595 

1:11.76 

1:11.925 

2:0.00 

2:0.255 

2:0.42 

2:0  585 

2:0.75 

2: 0.915 

2:1  08 

2:1  215 


6.25 
6.30 
6.35 
6.40 
6  45 
6.50 
6.55 
6.60 
6.65 
6.70 
6.75 
6.80 
6.85 
6  90 

6  95 

7  00 
7.05 
7  10 
7.15 
7  20 
7.25 
7  30 
7.35 
7  40 
7  45 
7  50 
7  55 
7.60 
7  05 


3.75 
3.78 
3.81 
3.84 
3.87 
3.90 
3.93 
3.96 

3  99 

4  02 
4.05 
4.08 
4.  11 
4  14 
4.17 
4.20 
4  23 
4.26 
4  20 
4  32 
4.35 
4  38 
4.41 
4  44 
4  47 
4.50 
4.53 
4.56 
4.59 


c  o  o  • 
c  -  . 


o  ^ 


2  a  ? 


C  3 


z  IC 


1  'f-  z~ 


7:11  625 
8:0.39 
8:1.155 
8:1.92 
8:2  685 
8:3.45 
8:4.215 
8:4  98 
8:5.745 
8:6  51 
8:7.275 
8: 8 . 04 
8:8  805 
8:9  57 
8:10  335 
S:  11 . 10 
S:  11  865 
9:0  63 
9:1.395 
9:2  16 
9:2.925 
9: 3 . 69 
9:4  455 
9:5.22 
9:5.985 
9:6  75 
9:7.515 
9:8  28 
9:9.045 


5£ 


W  3 


1:8.625 
1:8.79 
1:8.955 
1:9.12 
1:9  285 
1:9  45 
1:9.615 
1:9.78 
1:9.945 
1:10  11 
1:10  27  5 
1: 10.44 
1:10.  ()i)5 
1:10.7/ 
1:10  935 
1:11.10 
1:11.265 
1:11  43 
1:11.595 
1:11  70 
1:11.925 
2:0  09 
2:0  255 
2:0  42 
2:0  585 
2:0  75 
2:0  015 
2:1.08 
2:1.245 


&%  be 

g  %z 


9:8  25 

9:9.18 

9:10.11 

9:11.04 

9:11  97 

10:0.90 

10:1.83 

10:2.76 

10:3.69 

10:  1.62 

10: 5  55 

10:6  48 

10:7.41 

10:8  34 

10:9.27 

10:10.20 

10:11  13 

11:0.06 

11:0.99 

11:1. 92 

11:2.85 

11:3  78 

11:4  71 

11:5.64 

11:6.57 

11:7.50 

11:8.43 

11:9.36 

11:10.29 


7. 


ARCHITECTURAL  PROPORTION. 


32 


TABLE  OF  COLUMN  FINISH. — Continued. 


Length  of  Shaft. 

Diameter  of  Shaft 
above  Base 

Diameter  of  Shaft 
at  Neck 

Height  of  Capital 

Height  of  Shaft 
Base 

Whole  height  of 
Pedestal. 

Height  of 
Pedestal  Base. 

Height  of 
Pedestal  Cornice. 

Distance  from 
Floor  Line  to 

Lowrst  Line  (it 

Entablature. 

Height  of 
Entablature. 

Whole  height  of 
Column. 

One  Minute. 

7:8.40 

9.24 

7.70 

10.78 

5.541 

2:1.41 

7.70 

4.62 

9:9.81 

2:1.41 

11: 11 . 22 

.154 

7:9.00 

9  30 

7.75 

10.85 

5.58 

2: 1 . 575 

7.75 

4.65 

9: 10.575 

2: 1 . 575 

12:0.15 

.  155 

7: 9 . 60 

9.36 

7.80 

10.92 

5.616 

2:1.740 

7.80 

4  68 

9: 11 . 34 

2: 1 . 740 

12:1  08 

.156 

7: 10 . 20 

9.42 

7.85 

10  99 

5.652 

2: 1 . 905 

7.85 

4.71 

10:0.105 

2:1.905 

12:2.01 

157 

7: 10.80 

9.48 

7.90 

11.06 

5.688 

•2:2.07 

7.90 

4.74 

10:0.87 

2:2.07 

12:2.94 

.158 

7:11 .40 

9.54 

7.95 

11 . 13 

5.724 

2: 2 . 235 

7.95 

4.77 

10:1.635 

2:2.235 

12:3.87 

.159 

8: 0 . 00 

9.60 

8  00 

11.20 

5.76 

2: 2 . 40 

8.00 

4.80 

10:2.40 

2:2.40 

12:4.80 

.100 

8: 0 . 60 

9.66 

8  05 

11.27 

5.796 

2:2.565 

8.50 

4.83 

10:3.165 

2:2.565 

12:5.73 

161 

8: 1 . 20 

9  72 

8.10 

11.34 

5.832 

2:2.73 

8.10 

4.86 

10:3.93 

2:2.73 

12:6.66 

.162 

8: 1 . 80 

9.78 

8.15 

11.41 

5.868 

2:2.895 

8.15 

4.89 

10:4.695 

2:2.895 

12:7.59 

.163 

8: 2 . 40 

9.84 

8.20 

11.48 

5.904 

2:3.06 

8.20 

4  92 

10:5.46 

2:3.06 

12:8.52 

.164 

8: 3 . 00 

9.90 

8.25 

11.55 

5.94 

23.225 

8.25 

4.95 

10:6.225 

2:3.225 

12:9.45 

.165 

8: 3 . 60 

9.96 

8.30 

11.62 

5.976 

2: 3 . 39 

8.30 

4.98 

10:0.99 

2:3.39 

12: 10.38 

.166 

8:4.20 

10.02 

8.35 

11.69 

6.012 

2:3.555 

8.35 

5.01 

10:7.755 

2:3.555 

12:11.31 

.167 

8: 4 . 80 

10.08 

8.40 

11.76 

6  048 

2:3.72 

8  40 

5  04 

10:8.52 

2:3.72 

13:0.24 

.168 

8: 5 . 40 

10.14 

8 . 45 

11.83 

6.084 

2:3.885 

8.45 

5.07 

10:9  285 

2:3.885 

13: 1 . 17 

.169 

8: 6 . 00 

10.20 

8.50 

11.9(1 

6.12 

2:4  05 

8.50 

5  10 

10:10.05 

2:4.05 

13:2.10 

.170 

8: 6 . 60 

10.26 

8.55 

11 . 97 

6.156 

2:4.215 

8.55 

5.13 

10:10.815 

2:4.215 

13:3.03 

.171 

8: 7 . 20 

10 . 32 

8.60 

12.04 

6  192 

2:4.38 

8.60 

5.16 

10:11.58 

2:4.38 

13:3.98 

.172 

8:7.80 

10.38 

8  65 

12.11 

6.228 

2:4.545 

8.65 

5.19 

11:0.345 

2:4.545 

13:4.89 

.173 

8:8.40 

10.44 

8.70 

12.18 

6 . 264 

2:4.71 

8.70 

5.22 

11:1  11 

2:4  71 

13:5.82 

.174 

8:9.00 

10.50 

8.75 

12.25 

6.30 

2:4.875 

8  75 

5.25 

11:1.875 

2:4.875 

13:6.75 

.175 

8:9.60 

10.56 

8.80 

12.32 

6.336 

2:5.04 

8.80 

5  28 

11:2.64 

2:5.04 

13:7.68 

.176 

8:10.20 

10.62 

8  85 

12.39 

6  372 

2:5.205 

8.85 

5.31 

11:3.405 

2:5.205 

13:8.61 

.177 

8:10.80 

10.68 

8.90 

12.46 

6.408 

2:5.37' 

8.90 

5  34 

11:4  17 

2:5.37 

13:9.54 

.178 

8:11.40 

10.74 

8.95 

12.53 

0.444 

2:5.535 

8.95 

5.37 

11:4.935 

2:5.535 

13:10.47 

.179 

9:0.00 

10  80 

9.00 

12.60 

6.48 

2:5.70 

9  00 

5.40 

11:5.70 

2:5.70 

13:11.40 

.180 

9:0.60 

10.86 

9.05 

12.67 

6.516 

2:5.865 

9.05 

5.43 

11:6.465 

2:5.865 

14:0.33 

181 

9: 1 . 20 

10.92 

9.10 

12.74 

6.552 

2:6.03 

9.10 

5.46 

11:7  23 

2: 6.0:; 

14:1.26 

.182 

Length  of  Interior 
Window  Casing. 

Distance  from 
Floor  Line  to 
Top  of  Window- 
Stool. 

Height  of  Room 
Base  or  Skirting. 

Height  of 
Window- Stool 
or  Sill. 

Height  of 
Exterior  Doors. 

Distance  from 
Window  Si  >ftit  to 
Ceiling. 

Clear  height  of 
Story. 

ARCHITECTURAL  PROPORTION. 


33 


TABLE  OF  COLUMN  PIXISH.— Continued. 


.3 

til 

M 

h) 

J5  ■ 

i  % 

i  ° 

i.  0 

a 

5  d 

5 

c  o 
3  >5 

5 

Tr. 

w 

02  . 

c  30 

33 

■JL. 

W 

3 
A  r-J 

T  i 
^  u 

<u 

li 

o 

°  3 

'a)  .5 
—  /. 

HH  0 

0) 

p-l 

5  o  °3  ■ 
3  —  .  ? 

8333 

tc  5  2  = 

o 

o 

oc  a 
-  — 

s 

a 

O 
Q 

9:1  80 

10 

98 

9 

15 

12 

81 

6 

.588 

2: 6 . 195 

9.15 

5.49 

11:7.995 

2: 6 . 195 

14:2  19 

.183 

9: '2  40 

11 

04 

9 

20 

12 

88 

6 

624 

2:6  .36  . 

9  20 

5.52 

11:8.76 

2:6.36 

14:3.12 

.184 

9:3  00 

11 

10 

9 

25 

12 

95 

6 

.66 

2: 6 . 525 

9.25 

5  55 

11:9.525 

2:6.525 

14:4.05 

.185 

9: 3 .  GO 

11 

16 

9 

30 

13 

02 

6 

.696 

2:6  69 

9.30 

5.58 

11:10.29 

2:6.69 

14:4.98 

.186 

9:4.20 

11 

22 

9 

35 

13 

09 

6 

.732 

2:6.855 

9.35 

5.61 

11:11.0.55 

2:6.855 

14:5.91 

.187 

9:4.80 

11 

28 

9. 

40 

13 

10 

6 

.768 

2:7.02 

9.40 

5.64 

11:11.82 

2:7.02 

14:6.84 

.188 

9:5.40 

11 

34 

9 

45 

13 

23 

6 

.804 

2:7.185 

9.45 

5.67 

12:0.585 

2:7.185 

14:7.77 

.189 

.  9:6.00 

li 

40 

9. 

50 

13 

30 

6 

.84 

2: 7 . 35 

9.50 

5.70 

12:1.35 

2: 7 . 35 

14:8.70 

.190 

9:  G .  60 

11 

A  IX 

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Id 

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u 

.0(0 

2:7.515 

9.55 

5.73 

12:2  115 

2:7.515 

14:9.63 

.191 

9: 7 . 20 

11 

52 

9 

60 

13 

44 

6 

.912 

2:7.68 

9.60 

5.76 

12:2.88 

2:7.68 

14:10  56 

.192 

9:7.80 

11 

58 

9. 

65 

13 

51 

G 

.948 

2:7.845 

9.65 

5.79 

12:3.645 

2:7.845 

14:11  49 

.193 

9:8  40 

11 

04 

9. 

70 

13 

58 

6 

.984 

2: 8 . 01 

9.70 

5  82 

12:4.41 

2:8.01 

15:0  42 

.194 

9:9  00 

11 

70 

9. 

75 

13 

65 

7 

02 

2:8.175 

9.75 

5.85 

12:5.175 

2:8.175 

15:1.35 

.195 

9: 9.60 

11 

76 

9. 

80 

13 

72 

7 

.056 

2:8.34 

9.80 

5.88 

12:5.94 

2:8.34 

15:2.28 

.196 

9:10.20 

11 

82 

9 

85 

13 

79 

7 

.092 

2: 8 . 505 

9.85 

5.91 

12:6  705 

2:8.505 

15:3.21 

197 

9:10.80 

11 

88 

9. 

90 

13 

86 

7 

.128 

2:8.67 

9  90 

5.94 

12:7.47 

2:8  67 

15:4  14 

.198 

9:11.40 

11 

94 

9 

95 

13 

93 

7 

1(14 

2:8  835 

9  95 

5.97 

12:8.235 

2:8.835 

15:5.07 

.199 

10:0.00 

12 

00 

10 

00 

14 

00 

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Length  of  Interior 
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By  a  careful  examination  of  the  foregoing  tables,  any  one  at  all  familiar  with  design- 
ing or  building  houses  can  correctly  determine  the  proper  height  for  the  window  and 
exterior  door  openings,  the  height  of  the  room  base,  window-stool,  stucco  cornices,  etc. 
for  almost  every  height  of  story  that  could  lie  wanted.  When  the  height  of  the  story  has 
been  determined,  the  exact  size  of  the  members  of  mouldings,  etc.,  can  be  found  by 
simply  multiplying  the  number  of  minutes  contained  in  any  given  member  by  the  unit  of 
measure,  or  minute  given  in  the  last  column  of  figures  opposite  the  clear  height  of  the 
story. 


